When a Slack user responds to a thread of a BubbleIQ Zendesk ticket, you can choose to have that ticket post as a public response or internal note.
Open up a direct message with the BubbleIQ bot, and say "admin."
Under "A bubble's replies should be posted to Zendesk as:", click "Internal Note."
The bot should respond with a confirmation, and you're done! Messages will post from Slack to Zendesk as internal notes by default, unless they start with "PR:", then they will post as a public response.